I'm inclined to think the monitor cannot handle the refresh rate for the resolution you are trying to put it into. If the graphics card was failing then it either wouldn't have switched resolution or would not have returned to the correct resolution.
What settings do you have in display properties, settings, advanced, monitor? Do you have the "Hide modes this monitor cannot display" selected?
Try dropping the refresh rate down to 60Hz and then setting the 1024x768 resolution - If it doesn't work then a new monitor is likely to be the best option. Second hand at computer fairs works out at about £30-£50 for a 17" CRT.
Failing that get hold of some other software for the DVD writing - Nero usually has a free 30day trial version over on
www.ahead.deIf you are trying to convert video then the Nerovison express is reasonable too (don't know if that has a free trial version though)